Conference Venue Choice under Demand Uncertainty
EventCo must choose one venue for a one-day conference. Demand will be 200, 350, or 500 attendees, with probabilities 0.30, 0.50, and 0.20 respectively. Each attendee generates a contribution of $40. The Small venue has capacity 200 and fixed cost $4,000; Medium has capacity 350 and fixed cost $7,000; Large has capacity 500 and fixed cost $11,000. Attendees beyond capacity are turned away, and unused capacity cannot be resold. EventCo must commit to one venue now. A broker offers, for a non-refundable $1,500, an option to release 150 extra seats at whichever venue is chosen; the extra seats are useful only when demand exceeds the chosen capacity. The manager wants a formal expected-value analysis, an assessment of the value of perfect information, and advice on the broker's option.
1. Construct the payoff table and calculate the expected monetary value (EMV) of each venue.
Read the worked answer
Profit = $40 × minimum(demand, capacity) − fixed cost.
| Venue | Demand 200 | Demand 350 | Demand 500 | EMV |
|---|---|---|---|---|
| Small (cap. 200) | 4,000 | 4,000 | 4,000 | 4,000 |
| Medium (cap. 350) | 1,000 | 7,000 | 7,000 | 5,200 |
| Large (cap. 500) | −3,000 | 3,000 | 9,000 | 2,400 |
Workings: Small at demand 200 = 40(200) − 4,000 = 4,000; at higher demand it is capped at 200, so profit stays 4,000. Medium at 200 = 8,000 − 7,000 = 1,000; at 350 or 500 it is capped at 350, giving 14,000 − 7,000 = 7,000. Large at 200 = 8,000 − 11,000 = −3,000; at 350 = 14,000 − 11,000 = 3,000; at 500 = 20,000 − 11,000 = 9,000.
EMV(Small) = 4,000. EMV(Medium) = 0.30(1,000) + 0.50(7,000) + 0.20(7,000) = 5,200. EMV(Large) = 0.30(−3,000) + 0.50(3,000) + 0.20(9,000) = 2,400. Medium has the highest EMV.
2. Calculate the expected value of perfect information (EVPI) and apply the minimax regret criterion.
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With perfect information, choose the best venue for each demand state: demand 200 → Small ($4,000); demand 350 → Medium ($7,000); demand 500 → Large ($9,000).
EV with perfect information = 0.30(4,000) + 0.50(7,000) + 0.20(9,000) = 1,200 + 3,500 + 1,800 = $6,500. EVPI = 6,500 − 5,200 = $1,300. EventCo should pay no more than $1,300 for perfect demand information.
Regret table (best payoff in each state minus the payoff obtained):
| Venue | Demand 200 | Demand 350 | Demand 500 | Maximum regret |
|---|---|---|---|---|
| Small | 0 | 3,000 | 5,000 | 5,000 |
| Medium | 3,000 | 0 | 2,000 | 3,000 |
| Large | 7,000 | 4,000 | 0 | 7,000 |
Minimax regret selects Medium, because its worst regret of $3,000 is the smallest. This agrees with the EMV choice.
3. Evaluate the broker's option to release 150 extra seats for $1,500. Should EventCo buy it, and at what probability of demand 500 would it break even?
Read the worked answer
The extra seats matter only if demand exceeds capacity. For the Medium venue, demand 500 exceeds capacity by 150 seats. The extra contribution is 150 × $40 = $6,000; net of the $1,500 fee, the gain in that state is $4,500.
Expected net value of the option with Medium = 0.20(4,500) − 0.50(1,500) − 0.30(1,500) = 900 − 750 − 450 = −$300.
The option costs $1,500 in the 200 and 350 demand states but produces no benefit there. Its expected value is negative, so do not buy it. Break-even probability p of demand 500 satisfies 4,500p − 1,500 = 0, so p = 1/3 ≈ 0.333. Current probability is 0.20, well below break-even. The same logic should be checked for other venues, but Medium is the chosen venue, so the option is not worthwhile.